An isosceles triangle has a base of 12 cm with equal sides of 20 cm each. How do you determine the area of this triangle accurate to the nearest square centimeter?

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Answer 1 · 2018-02-22T13:44:18

See a solution process below:

The formula for the area of a triangle is:

#A = 1/2bh#

The base of this isosceles triangle is given as 12cm.

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Because the line which bisects and isosceles triangles is at a right angle to the base we can use the Pythagorean Theorem to find the height.

The Pythagorean Theorem states:

#a^2 + b^2 = c^2#

Where:

#a# and #b# are sides of a right triangle.

#c# is the hypotenuse of a right triangle.

In this problem, the hypotenuse, or #c#, is #20"cm"#

One side of the right triangle is the height which we need to solve for.

The other side of the right triangle for this isosceles triangle is #1/2# of the base, or, #6"cm"#

Substituting and solving for #a# gives:

#a^2 + (6"cm")^2 = (20"cm")^2#

#a^2 + 36"cm"^2 = 400"cm"^2#

#a^2 + 36"cm"^2 - color(red)(36"cm"^2) = 400"cm"^2 - color(red)(36"cm"^2)#

#a^2 + 0 = 364"cm"^2#

#a^2 = 364"cm"^2#

#sqrt(a^2) = sqrt(364"cm"^2)#

#a ~= 19"cm"#

Therefore the height is approximately: 19.08cm

We can now substitute into the formula for the area to determine the area of this triangle:

#A = 1/2 xx 12"cm" xx 19"cm"#

#A = 6"cm" xx 19"cm"#

#A = 114"cm"^2# accurate to the nearest square centimeter